What should come first ?

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Considering how far you are towing yours, I would check tires and lights.

Cleaning, always, always the first thing we have ever done, and we have always bought used, was thorough cleaning.

If the camper has an odd smell, Febreeze!  It does have a bit of a heavy smell at first, but it gets rid of the funny smells in fabrics, and makes everything so much nicer.

* Fridge ?  Go with coolers, we did fine with them until we got our current camper that had a real fridge, oh and we grew our family from four to six.  We also have a tall dorm fridge now, but we only take it when camping for four-five days or longer.  A good tip for using coolers?  Keep your milk jugs, or juice bottles etc, wash them then fill with water and freeze.  Us these for the food coolers instead of cubed ice, and you won't have problems keeping things cold, and you won't have watery mess in the bottom.  We also always froze all the meats that we were not using the first day.  I typically still had ice in the jugs when we would return, even from a four day trip in the Texas summer.  I separate the food from drinks as well, and food coolers are opened as little as possible.

* Brakes ?  Brakes, ok, guys, I don't want to be flamed, but we've owned three campers, and only the latest one had brakes.  I love having them now, but was fine without them until then.  Our oldest camper was a 1980 Stacraft Starmaster, and it didn't have brakes and would require a new axle to have them.  We didn't have any plans on adding them when it was stolen.  Our 1990 Starcraft was so light, we never worried about brakes as the tow vehicle had more than enough power to stop.

* Inside organizer thingie magicies from Wally world ?  Wait on these, you need to check out your options, and actually camp a few times to really see how you want these to work and what to buy.  Camp a couple of times at least before you invest in these.

* New covers for the mattresses and cushions ?
Cushions/mattresses, in our three purchases so far have never found any of these that I had to replace.  I had to pull off covers and wash them and use febreeze a couple times, but never replace.  I've also always added more to the mattresses with egg foam etc, but that was just because we like more softness.

* Converter ?  The camper doesn't have one in it I assume?  We have one but never use it, we don't dry camp.

* Battery ? Never had one, have never needed it, but if you plan on dry camping you should make it a priority.

* Furnace ?  Buy one or two ceramic heaters.  Furnaces will cost you a lot more than the electric heaters, and in my opinion, without something to help the air get out onto the bunks where you are, wouldn't help all that much.  We didn't have a furnace until our last camper, and always used two ceramic heaters, one pointed at each bunk, anybody sleeping in the body of the camper was warm even with the heaters pointed at the bunks.  We still have those heaters, and use them when fall camping if we have someone sleeping in tents.


Some things to consider that were not on your list.

Canvas, patching and waterproofing.  We had to waterproof both of our older campers.  We used tent seam sealer on the seams, and Scotchguard aerosol water repellent on the canvas, and we always were dry.

Chocks

Correct wiring connectors

Safety chains, the camper may not have them on there, as I recall all but the last one we have had to add them, and I think they are required by state law here, but the older two didn't have them.

A spare, a tire tool that will work with the camper, and a jack.  None of our campers have a jack, and I don't think our auto jacks will work with the camper.  We also didn't have a tire tool that would work.  We carry a two ton "floor" jack type model in the camper, with a break down four way tire tool.  We've had to use it several times, and were darned happy we had it each and every time.  We got a special deal and the whole thing fits in a storage bag that we keep accessible.

First Aid kit, have not been on a trip yet that we didn't need this!

Birol, we started out camping on a budget too, and we got most of our stuff at garage sales.  We still look there first for camping items, and then wal-mart/big lots/dollar store type places.  We have very few items that actually came from an RV store, and those are mainly parts for the camper that you can only get from an RV store.